Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
from math import *
EPSILON = 0.000000000001
n = int(raw_input())
found = False

for k in range(1,31623):
    x = n - k*(k+1)/2
    if x < 0: break
    a = 1.0
    b = 1.0
    c = -2.0*x
    
    det = b**2 -4*a*c
    if det >= 0:
        m = (-b + det**0.5)/2.0
        if m > 0 and (m-floor(m) <EPSILON or ceil(m)-m < EPSILON):
            found = True
            #print k,m
            break
        
if found:
    print "YES"
else:
    print "NO"